[zmgsabst]

My university had quarters, not semesters, but:

1. Derivatives

2. Integrals

3. Applications — function approximation; solids of rotation; vectors; etc.

4. Multivariate — partial derivatives, multiple integrals, etc.

Glancing at a nearby community college’s course catalog, they have similar split.

[fgh]

Does this include the full machinery to prove the necessary theorems or are these basically practical courses?

[zmgsabst]

Those are practical courses, meant to prep for linear algebra and differential equations — and various STEM tracks. As I recall, there were some proofs (eg, limits showing derivative rules; limits showing sums for integral rules).

We covered all the proofs in real analysis 1 (derivatives; sequences) and 2 (integrals; measure).